Online Variational Approximations to non-Exponential Family Change Point Models: With Application to Radar Tracking

Neural Information Processing Systems

The Bayesian online change point detection (BOCPD) algorithm provides an efficient way to do exact inference when the parameters of an underlying model may suddenly change over time. BOCPD requires computation of the underlying model's posterior predictives, which can only be computed online in $O(1)$ time and memory for exponential family models. We develop variational approximations to the posterior on change point times (formulated as run lengths) for efficient inference when the underlying model is not in the exponential family, and does not have tractable posterior predictive distributions. In doing so, we develop improvements to online variational inference. We apply our methodology to a tracking problem using radar data with a signal-to-noise feature that is Rice distributed. We also develop a variational method for inferring the parameters of the (non-exponential family) Rice distribution.


Air Traffic Controller Team Intent Inference

AAAI Conferences

This paper describes methods and applications of intent inference for future teams of air traffic controllers that include a strategic planning controller responsible for'conditioning' the traffic flow. The Crew Activity Tracking System (CATS) provides a framework for developing intent-aware intelligent agents to support controller teams. A proof-of-concept system provides reminders to the planner and another controller in real time. This team-level system draws upon related efforts to apply intent inference to better understand and model the planner's task. These efforts entail enhancing CATS with a model of perception of the traffic display, and using different model forms within the CATS framework. The paper describes, specifically, inferring the planner's strategy using a Bayesian Network model, and inferring the planner's immediate intent using a temporal Bayesian model. The paper relates these efforts, and the team-level reminder system, to other relevant research.


Flexible Models for Microclustering with Application to Entity Resolution

Neural Information Processing Systems

Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman-Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points. These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets.


Modeling Multi-Vehicle Interaction Scenarios Using Gaussian Random Field

arXiv.org Machine Learning

Autonomous vehicles (AV) are expected to navigate in complex traffic scenarios with multiple surrounding vehicles. The correlations between road users vary over time, the degree of which, in theory, could be infinitely large, and thus posing a great challenge in modeling and predicting the driving environment. In this research, we propose a method to reproduce such high-dimensional scenarios in a finitely tractable form by defining a stochastic vector field model in multi-vehicle interactions. We then apply non-parametric Bayesian learning to extract the underlying motion patterns from a large quantity of naturalistic traffic data. We use Gaussian process to model multi-vehicle motion, and Dirichlet process to assign each observation to a specific scenario. We implement the proposed method on NGSim highway and intersection data sets, in which complex multi-vehicle interactions are prevalent. The results show that the proposed method is capable of capturing motion patterns from both settings, without imposing heroic prior, hence can be applied for a wide array of traffic situations. The proposed modeling can enable simulation platforms and other testing methods designed for AV evaluation, to easily model and generate traffic scenarios emulating large scale driving data.


Bayesian Non-Homogeneous Markov Models via Polya-Gamma Data Augmentation with Applications to Rainfall Modeling

arXiv.org Machine Learning

Discrete-time hidden Markov models are a broadly useful class of latent-variable models with applications in areas such as speech recognition, bioinformatics, and climate data analysis. It is common in practice to introduce temporal non-homogeneity into such models by making the transition probabilities dependent on time-varying exogenous input variables via a multinomial logistic parametrization. We extend such models to introduce additional non-homogeneity into the emission distribution using a generalized linear model (GLM), with data augmentation for sampling-based inference. However, the presence of the logistic function in the state transition model significantly complicates parameter inference for the overall model, particularly in a Bayesian context. To address this we extend the recently-proposed Polya-Gamma data augmentation approach to handle non-homogeneous hidden Markov models (NHMMs), allowing the development of an efficient Markov chain Monte Carlo (MCMC) sampling scheme. We apply our model and inference scheme to 30 years of daily rainfall in India, leading to a number of insights into rainfall-related phenomena in the region. Our proposed approach allows for fully Bayesian analysis of relatively complex NHMMs on a scale that was not possible with previous methods. Software implementing the methods described in the paper is available via the R package NHMM.